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      <h2>Summary of Tao Solvers</h2>
      <h3>Requests and contributions welcome</h3>

      <table border="1" summary="Summary of Tao Solvers Available from PETSc">

        <thead>
          <tr>
            <th></th>
            <th>Algorithm</th>
            <th>Objective</th>
            <th>Gradient</th>
            <th>Hessian</th>
            <th>Constraints</th>
            <th>Jacobian</th>
            <th>Constraint type</th>
          </tr>
        </thead>

        <!-- The tfoot *must* be before tbody!!!! 
        <tfoot>
          <tr>
            <td colspan="8">

              <p>
                <a name="relax">**</a> A "block Jacobi" style SOR with lits local
                smoothing followed by update of ghost points from other processors, see
                <a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSOR.html">MatSOR()</a>
              </p>

              <p><a name="pbrelax">***</a> Use PCType of PCSOR</p>

            </td>
          </tr>
        </tfoot>
        -->

        <tbody>
          <tr>
            <td>Unconstrained</td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/Nelder-Mead.html">Nelder-Mead</a></td>
            <td>X</td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
          </tr>

          <tr>
            <td></td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/taocg.html">conjugate gradient</a></td>
            <td>X</td>
            <td>X</td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
          </tr>

          <tr>
            <td></td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/lmvm.html">limited memory variable metric (quasi-Newton)</a></td>
            <td>X</td>
            <td>X</td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
          </tr>

          <tr>
            <td></td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/owlqn.html">owlqn</a></td>
            <td>X</td>
            <td>X</td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
          </tr>

          <tr>
            <td></td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/bmrm.html">bmrm</a></td>
            <td>X</td>
            <td>X</td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
          </tr>

          <tr>
            <td></td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/nls.html">Newton line search</a></td>
            <td>X</td>
            <td>X</td>
            <td>X</td>
            <td></td>
            <td></td>
            <td></td>
          </tr>

          <tr>
            <td></td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/ntr.html">Newton trust region</a></td>
            <td>X</td>
            <td>X</td>
            <td>X</td>
            <td></td>
            <td></td>
            <td></td>
          </tr>

          <tr>
            <td></td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/ntl.html">Newton trust region with linesearch</a></td>
            <td>X</td>
            <td>X</td>
            <td>X</td>
            <td></td>
            <td></td>
            <td></td>
          </tr>

          <tr>
            <td>Bound Constrained</td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/blmvm.html">bounded limited memory variable metric (quasi-Newton)</a></td>
            <td>X</td>
            <td>X</td>
            <td></td>
            <td></td>
            <td></td>
            <td>Box constraints</td>
          </tr>

          <tr>
            <td></td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/gpcg.html">gradient projection conjugate gradient</a></td>
            <td>X</td>
            <td>X</td>
            <td></td>
            <td></td>
            <td></td>
            <td>Box constraints</td>
          </tr>

          <tr>
            <td></td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/bqpip.html">bounded quadratic interior point</a></td>
            <td>X</td>
            <td>X</td>
            <td></td>
            <td></td>
            <td></td>
            <td>Box constraints</td>
          </tr>

          <tr>
            <td></td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/tron.html">tron</a></td>
            <td>X</td>
            <td>X</td>
            <td>X</td>
            <td></td>
            <td></td>
            <td>Box constraints</td>
          </tr>

          <tr>
            <td>Complementarity</td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/asfls.html">active-set feasible line search</a></td>
            <td></td>
            <td></td>
            <td></td>
            <td>X</td>
            <td>X</td>
            <td>Complementarity</td>
          </tr>

          <tr>
            <td></td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/asils.html">active-set infeasible line search</a></td>
            <td></td>
            <td></td>
            <td></td>
            <td>X</td>
            <td>X</td>
            <td>Complementarity</td>
          </tr>

          <tr>
            <td></td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/ssfls.html">semismooth feasible line search</a></td>
            <td></td>
            <td></td>
            <td></td>
            <td>X</td>
            <td>X</td>
            <td>Complementarity</td>
          </tr>

          <tr>
            <td></td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/ssfls.html">semismooth infeasible line search</a></td>
            <td></td>
            <td></td>
            <td></td>
            <td>X</td>
            <td>X</td>
            <td>Complementarity</td>
          </tr>

          <tr>
            <td>Nonlinear Least-squares</td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/pounders.html">POUNDERS</a></td>
            <td>X</td>
            <td></td>
            <td></td>
            <td></td>
            <td></td>
            <td>Box constraints</td>
          </tr>

          <tr>
            <td>PDE-constrained</td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/lcl.html">linearly constrained lagrangian</a></td>
            <td>X</td>
            <td>X</td>
            <td>X</td>
            <td>X</td>
            <td>X</td>
            <td>PDE constraints</td>
          </tr>

          <tr>
            <td>Constrained</td>
            <td><a href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Tao/ipm.html">interior point method</a></td>
            <td>X</td>
            <td>X</td>
            <td>X</td>
            <td>X</td>
            <td>X</td>
            <td>general constraints</td>
          </tr>

        </tbody>
      </table>

      <p>
        This page was inspired by <a href="http://www.netlib.org/utk/people/JackDongarra/la-sw.html">Jack Dongarra's freely available software for linear algebra list</a>
      </p>

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